All the organic-rich shale samples were black mud shales of the lower Silurian Longmaxi Formation widely developed in the Upper Yangtze Platform, south China. JING-1, JING-2, and JING-3 were from Jingmen region, Hubei Province; YS106 and YS109 were from Yibin region, Sichuan Province and YANG102 was from Luzhou region, Sichuan Province. Prior to measurement, 100 g of each sample was ground into powder of 60 - 80 mesh size. These powder samples were prepared for analysis of total organic carbon (TOC), rock pyrolysis, vitrinite reflectance test, X-ray diffraction (XRD), high pressure mercury test and N₂/CO₂ adsorption.

WR-112 Laboratory Equipment Corporation (LECO) carbon analyzer of LECO Company, America was used to conduct the organic carbon analysis. The size of the sample particle is less than 0.2 mm. Iron and tungsten were added into the sample particle to aid combustion.

External standard analysis of the OGE workstation was used to conduct the continuous rock pyrolysis test, in which the first step was to heat to 300˚C and then to 500˚C.

UMSP-50 micro spectrophotometer was used to test vitrinite reflectance. The test conditions were temperature under 26˚C, a wavelength of 546 nm ± 5 nm (green), and ×25 to ×100 unstrained oil immersion objective. One hundred tungsten halogen lamps and electronic exchange regulator of 3 kVA were also used.

The mineral composition test was done using XRD under Cu-Kα radiation. Emission and scattering slits are both 1˚, and the receiving slit is 0.3 mm. The operating voltage is 30 KV - 45 KV, and the electric current is 20 mA - 100 mA; the scanning speed is 2˚/min, and the sampling step width is 0.02˚.

The Quadrasorb evo of Quantachrome, American was used to test mesopores structure and part of masopores structure by N₂ adsorption method. Before the test, all the samples were constant temperature dried under 105˚C and vacuum, the adsorption gas purity is 99.99% and the experimental temperature is 77.35 K.

The Autosorb-iQ of Quantachrome, American was used to test micropores structure by CO₂ adsorption method. After degassing treatment, all shale samples were tested under 273.15 K.

The volumetric method is commonly used in isothermal adsorption experiments on CBM and shale gas [20] [21] [22] . The principle of volumetric method is to calculate the adsorption volume according to the change of pressure.

In this study, the method selected to conduct the isothermal adsorption and desorption experiments is the gravimetric method with magnetic suspension balance (MSB; Figure 1). The weight of the shale sample was balanced using a

non-contact suspending coupling mechanism. The balance has zero point and measuring point, and the two states automatically switch regularly to remove the inherent negative effects from zero drift effectively (reaching 0.00001 g accuracy). This design can achieve high precision measurement. The experiment process includes blank test, sample pretreatment, buoyance test, isothermal adsorption test, isothermal desorption test and data treating. Blank test tested without any sample in container and sample pretreatment avoided the influence from water and other gases aim to decrease the error. Shale samples were pretreated under 105˚C and vacuumed before the isothermal adsorption experiment. The buoyance test was tested with helium to calibrate the buoyance of samples and container suffered after the pretreatment, which can calculate the adsorption volume accurately.

The adsorbed gas is 99.8% pure methane, and the experiment temperature is 30˚C, and the shale samples were pulverized to 0.18 mm. The selected pressure points were 0 MPa, 0.5 MPa, 1 MPa, 2 MPa, 3 MPa, 4 MPa, 6 MPa, 10 MPa, 15 MPa, 20 MPa, 25 MPa, 30 MPa, and 33 MPa, respectively.

Desorption experiments were conducted under the same conditions as the adsorption experiments, except for the pressure setting. The selected pressure points for desorption were 33 MPa, 30 MPa, 25 MPa, 20 MPa, 15 MPa, 10 MPa, 6 MPa, 4 MPa, 3 MPa, 2 MPa, 1 MPa, 0.5 MPa, and 0 MPa, respectively.

Table 1 shows that organic carbon content of the shale samples is 0.22% - 4.17% with an average of 1.92%. The organic matter type II1 indicates the high degree of organic matter maturity. The results of vitrinite reflectance are 1.92%-2.45% with an average of 2.11%, also indicating the high degree of organic matter maturity. Clay mineral content is 29.9% - 53.5% with an average of 42.0%. Table 2 show the low temperature N₂ adsorption and CO₂ adsorption results, Figure 2

and Figure 3 respectively represent the pore size distribution micropores and mesopores. The pore volume of BJH method ranged from 0.003 cm³/g - 0.017 cm³/g, DFT method ranged from 0.002 cm³/g - 0.191 cm³/g. BJH method is used

for calculate mesopore and a part of macropore. DFT method is used for calculate micropore and mesopore. Combining with the results in Table 2, Figure 2 and Figure 3, it is shown that both method are similarity and the result of pore width is small. Therefore micropores developed well in the shale samples. The specific surface area of micropores ranged from 3.77 m²/g - 21.75 m²/g is larger than mesopores ranged from 1.22 m²/g - 8.39 m²/g in shale samples. Micropores controlled the adsorption process and had larger specific surface area, thus it was benefit to adsorb shale gas.

MSB was used for the isotherm adsorption experiments. The results are listed in Figure 4, which shows that the adsorption volume increases rapidly at 0 MPa - 10 MPa. Micropores play a major role in the adsorption process, and the potential field of adjacent hole walls overlap. The adsorbed energy of the gas molecules is high; thus, the adsorption volume of the micropore filling is large [8] . The adsorption volume increases gradually at 10 MPa - 25 MPa, where in the mesopores begin to assume a major role. The specific surface and gravity of the wall of the hole is smaller than micropore, thus, adsorption velocity becomes slow. The adsorption volume nearly remained unchanged after 25 MPa; microporous and mesoporous adsorptions all reached saturation. Macropores have a large diameter, and gas molecules exist freely in them. Thus, the volume of adsorbed gas molecules, as well as the adsorption volume, does not increase.

Desorption is the inverse process of adsorption. MSB is also used to conduct the desorption experiments. Desorption velocity, which is an important parameter of shale gas desorption, is the ratio of desorbed gas volume to time [23] [24] [25] . The expression is

v = V / t (1)

where v represents the desorption rate (mL/g・h⁻¹), V represents the desorption volume (mL/g), and t represents the time interval for desorption balance(h). The curves of isothermal desorption and desorption velocity are shown in Figure 5. Figure 6 shows that when the pressure is high (33 MPa - 10 MPa), desorption velocity is small and remains at a relatively stable level. Desorption rate rises rapidly when pressure falls to 10 MPa, indicating that 10 MPa - 0.5 MPa is the main period of shale gas desorption.

Langmuir, Freundlich, Langmuir-Freundlich, D-R, and Toth equations are commonly used for isotherm adsorption to fit the adsorption curves [26] [27] . In addition, semi-pore equation is also used in this study to select out the best equation among the ones stated above. The equations are listed in Table 3 [13] [28] [29] [30] [31] .

V_L and V₀ are the saturated adsorption capacity (mL/g); P_L represents the Langmuir pressure (MPa); K represents the empirical constant; x represents the constant, x < 1; m is the heterogeneity parameter of adsorbent, m ≤ 1; b = 1/P_L; D is the constant of the adsorbent; P_S denotes the saturated vapor pressure (MPa); α represent the parameters relative to the adsorbent or adsorbate property. k is the constant of inhomogeneity of adsorbent. Table 3 shows that the Langmuir, Freundlich, and D-R equations comprise two parameters, whereas Langmuir-Freundlich, semi-pore, and Toth equations have three. Among these equations, Langmuir is the simplest and considers the monolayer adsorption on the adsorbent surface in the adsorption process. D-R equation is based on the micropore filling theory and is more suitable for microporous solids. The semi-pore equation, which can also be used in the study of shale gas, is proposed in the CBM research, and is based on the characteristics of irregular and porous

pore structure. Freundlich, Langmuir-Freundlich, and Toth equations are either empirical or semi-empirical. Fitting results of these equations are shown in Figure 6 and Table 4.

Note: Ads = adsorption; Des = desorption.

As shown in Figure 6, the results of all the isothermal equations fit well. Langmuir, semi-pore, and Toth equations are better than Freundlich and D-R equations. Relative errors were calculated to determine the best fitting equation for isothermal adsorption process, as shown in Figure 7.

Figure 7 shows that the best equation for fitting in the isothermal adsorption process is the semi-pore equation, which has a relative fitting error of under 5%. Fitting results of the three-parameter equations are better than the two-parameter ones, because there a parameter relative to non-uniformity of the shale surface exists in the three-parameter equations. The presence of the third parameter reduces the error more effectively. The Langmuir equation is the most widely used equation because of its simple expression, physical meaning of its parameters, and good fitting results.

The Langmuir, Freundlich, Langmuir-Freundlich, D-R, Toth, and semi-pore equations were also used to fit the desorption curves. V_L of desorption fitting is compared with that of adsorption fitting. The fitting results of desorption and comparison results are shown in Figure 8 and Table 4, respectively.

Desorption fitting results are similar to adsorption, with the Langmuir-Freundlich, semi-pore, and Toth equations as the best fitting equations. As shown in Table 4, the V_L of the desorption process is larger than that of the adsorption one, which is called desorption hysteresis. This result is probably due to

the capillary condensation in the pores of the shales or the changed pore structures during adsorption. The specific reasons need to be further studied.

Adsorption potential theory is proposed by Polanyi for physical adsorption process, which was expressed as [32]

ε = ∫ P P s V d P = ∫ P P s R T P d P = R T ln ( P s / P ) (2)

where ε represents adsorption potential (J/mol), V is the gas volume of free state (cm³/g), P_S is the saturated vapor pressure (MPa) when the temperature is T, P is the balance pressure(MPa), T is the temperature of experiment (K), and R is gas constant(J/mol・K⁻¹).

When the experimental temperature is more than the critical temperature, the concept of saturation vapor pressure at above the critical temperature does not exist, that is to say, the saturation vapor pressure lose physical meaning. Thus, an experience formula established by Dubinin is used to calculate the virtual saturation vapor pressure P_V of methane in supercritical condition. The equation is showed as [33] .

P v = P c [ T T c ] 2 (3)

where P_c is supercritical pressure (MPa), and T_c is supercritical temperature(K). Adsorption potential becomes large with the decrease of distance between gas molecules and shale surface. Potential field direction is determined from the adsorption phase to bulk phase. Adsorption potential can be expressed as the distance by the adsorbate molecule from its site to zero point. The gas molecule is in free state when adsorption potential is negative and is in adsorption state when adsorption potential is positive.

The adsorption potential theory was used to explain the shale isotherm factors, and it was also used to explain desorption process and estimate the degree of difficulty of different shale samples.

Saturated vapor pressures of methane at 30˚C, 50˚C, 70˚C, and 90˚C were 11.68 MPa, 13.28 MPa, 14.99 MPa, and 16.80 MPa, respectively. The adsorption potential and adsorption results of JING-1 at different temperatures are shown in Figure 9.

Figure 9 shows that the adsorption potential becomes larger with the increase of temperature at the same pressure. Thus, the attraction from adsorbent surface becomes larger and more prone to adsorption. Meanwhile, the isothermal adsorption curve at 30˚C is much higher than others. With temperature increasing, potential energy also increase when gas molecules move to the solid surface of shale from bulk phase to adsorbed phase. In theory, the increase in temperature would benefit the adsorption. However, the thermal motion of gas molecules also rises up and plays a greater influence. Comparing with the relationship

among adsorption volume, temperature and potential energy, it is obvious that temperature has a great influence on adsorption volume, little effect on potential energy.

JING-1, JING-2, and JING-3 samples have different TOC. The adsorption potential of these samples, when the adsorption volumes are 0.20 mL/g, 0.30 mL/g, 0.50 mL/g, 0.60 mL/g, and 0.70 mL/g, respectively, are shown in Figure 10. As shown in Figure 10, the adsorption potential becomes larger with the increase of TOC when the adsorption volume is constant. A greater adsorption potential also means a greater attraction between adsorption surface and gas molecules. Thus, the adsorption capacity of JING-1 sample is best.

Figure 11 shows the results of adsorption of shale with and without moisture. The moisture sample was prepared according to the standards of the American Society for Testing and Materials [12] . The shale samples were placed into water for 2 h to 3 h, underwent vacuum suction, and then placed in a vacuum dryer (within supersaturated solution of potassium sulfate). The evacuation condition is 20 kPa, and the samples were weighted every 24 h until the weight of two adjacent samples is less than 2%.

The critical temperature of methane is −82.6˚C, over this temperature the state is called supercritical state. When the experimental temperature is more than the critical temperature, the concept of saturation vapor pressure at above the critical temperature does not exist, that is to say, the saturation vapor pressure lose physical meaning. In this manuscript, the adsorption capacity is regarded as excess adsorption, and it is greater than absolute adsorption. As shown in Figure 11, the adsorption capacity of the moisturized sample is remarkably smaller than the dried sample, because the saturation vapor pressure of the mixed gas of methane and vapor is significantly smaller than pure methane.

The curves of adsorption potential and desorption velocity are shown in Figure 12. The adsorption potential curves have the same trend with desorption velocity curves. When pressure is high, the adsorption potential of gas molecules is negative and its existence state is free. Moreover, under this condition, slight desorption and small desorption velocity were present. When pressure dropped to 10 MPa, the adsorption potential of gas molecules began to become positive with an absorbed state. Thereafter, the adsorbed molecules started to escape; the volume

of desorbed gas became high, and desorption velocity began to increase rapidly. The maximum slopes of adsorption potential curves emerge in the range from 10 MPa - 0.5 MPa, and desorption velocity also began to increase rapidly at the same time.

The relationship of cumulative volume of desorption gas and adsorption potential is shown in Figure 13. The horizontal line represents the cumulative volume of desorption gas, which is 0.20 mL/g. The relationship of adsorption potential is YS106 > JING-3 > JING-2 > YS109 > YANG102 > JING-1 when the cumulative adsorption is identical. Among the samples, JING-1 was most prone to desorption, and YS106 was the most difficult to desorbed.